Tomasz Penza (Warsaw University of Technology, Poland), Sufficient conditions for a Maltsev product of two varieties to be a variety

Tue, 10 Oct 2023, 1:25 pm MDT

The Maltsev product $\mathcal{V} \circ \mathcal{W}$ of varieties $\mathcal{V}$ and $\mathcal{W}$ of a type $\Omega$ is a class that consists of all algebras $A$ of the type $\Omega$, which have a congruence $\theta$ such that the quotient $A/\theta$ belongs to $\mathcal{W}$ and each congruence class of $\theta$ which is a subalgebra of $A$ belongs to $\mathcal{V}$. The class $\mathcal{V} \circ \mathcal{W}$ is closed under subalgebras, direct products, and isomorphic images. However it may not be closed under homomorphic images, and so it may not be a variety. I will present a new sufficient condition for $\mathcal{V} \circ \mathcal{W}$ to be a variety and I will discuss various cases in which this sufficient condition is satisfied.

[slides] [video]